An axiomatic approach to function spaces was developed in [1]}, [2]}.
A more general (than \(L_{p}\) ) function space satisfying a certain set of axioms was used on the right of (REF ).
This approach is capable of dealing with weighted Besov spaces of variable smoothness \(\lbrace s_{k}\rbrace  \in Y^{\alpha _{3}}_{\alpha _{1},\alpha _{2}}\) 
(with weights satisfying the doubling property).
